Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources

Article metrics


X-ray radiographic absorption imaging is an invaluable tool in medical diagnostics and materials science. For biological tissue samples, polymers or fibre composites, however, the use of conventional X-ray radiography is limited due to their weak absorption. This is resolved at highly brilliant X-ray synchrotron or micro-focus sources by using phase-sensitive imaging methods to improve the contrast1,2. However, the requirements of the illuminating radiation mean that hard-X-ray phase-sensitive imaging has until now been impractical with more readily available X-ray sources, such as X-ray tubes. In this letter, we report how a setup consisting of three transmission gratings can efficiently yield quantitative differential phase-contrast images with conventional X-ray tubes. In contrast with existing techniques, the method requires no spatial or temporal coherence, is mechanically robust, and can be scaled up to large fields of view. Our method provides all the benefits of contrast-enhanced phase-sensitive imaging, but is also fully compatible with conventional absorption radiography. It is applicable to X-ray medical imaging, industrial non-destructive testing, and to other low-brilliance radiation, such as neutrons or atoms.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Talbot–Lau-type hard-X-ray imaging interferometer.
Figure 2: X-ray images and section profiles of a test sample containing one PTFE and two PMMA spheres, retrieved from image data recorded with a standard X-ray tube operated at 40 kV/25 mA.
Figure 3: X-ray images of a small fish retrieved from image data recorded with a standard X-ray tube operated at 40 kV/25 mA.


  1. 1

    Fitzgerald, R. Phase-sensitive X-Ray imaging. Phys. Today 53, 23–27 (2000).

  2. 2

    Momose, A. Phase-sensitive imaging and phase tomography using X-ray interferometers. Opt. Express 11, 2303–2314 (2003).

  3. 3

    Bonse, U. & Hart, M. An x-ray interferometer with long separated interfering beam paths. Appl. Phys. Lett. 6, 155–156 (1965).

  4. 4

    Momose, A., Takeda, T., Itai, Y. & Hirano, K. Phase-contrast X-ray computed tomography for observing biological soft tissues. Nature Med. 2, 473–475 (1996).

  5. 5

    Ingal, V. N. & Beliaevskaya, E. A. X-ray plane-wave topography observation of the phase contrast from a non-crystalline object. J. Phys. D 28, 2314–2317 (1995).

  6. 6

    Davis, T. J., Gao, D., Gureyev, T. E., Stevenson, A. W. & Wilkins, S. W. Phase-contrast imaging of weakly absorbing materials using hard X-rays. Nature 373, 595–598 (1995).

  7. 7

    Chapman, L. D. et al. Diffraction enhanced x-ray imaging. Phys. Med. Biol. 42, 2015–2025 (1997).

  8. 8

    Snigirev, A., Snigireva, I., Kohn, V., Kuznetsov, S. & Schelokov, I. On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Rev. Sci. Instrum. 66, 5486–5492 (1995).

  9. 9

    Wilkins, S. W., Gureyev, T. E., Gao, D., Pogany, A. & Stevenson, A. W. Phase-contrast imaging using polychromatic hard X-rays. Nature 384, 335–337 (1996).

  10. 10

    Cloetens, P. et al. Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl. Phys. Lett. 75, 2912–2914 (1999).

  11. 11

    Nugent, K. A., Gureyev, T. E., Cookson, D. F., Paganin, D. & Barnea, Z. Quantitative phase imaging using hard X rays. Phys. Rev. Lett. 77, 2961–2964 (1996).

  12. 12

    Mayo, S. C. et al. X-ray phase-contrast microscopy and microtomography. Opt. Express 11, 2289–2302 (2003).

  13. 13

    Peele, A. G., De Carlo, F., McMahon, P. J., Dhal, B. B. & Nugent, K. A. X-ray phase contrast tomography with a bending magnet source. Rev. Sci. Instrum. 76, 083707 (2005).

  14. 14

    Als-Nielsen, J. & McMorrow, D. Elements of Modern X-Ray Physics (Wiley, New York, 2001).

  15. 15

    McMahon, P. J., Allman, B. E., Arif, M., Werner, S. A. & Nugent, K. A. Quantitative phase radiography with polychromatic neutrons. Phys. Rev. Lett. 91, 145502 (2003).

  16. 16

    Keren, E. & Kafri, O. Diffraction effects in moire deflectometry. J. Opt. Soc. Am. A 2, 111–120 (1985).

  17. 17

    Kafri, O. & Glatt, I. The Physics of Moire Metrology (Wiley, New York, 1990).

  18. 18

    Ress, D. et al. Measurement of laser-plasma electron density with a soft x-ray laser moire deflectometer. Science 265, 514–517 (1994).

  19. 19

    Weitkamp, T. et al. Hard X-ray phase imaging and tomography with a grating interferometer. Proc. SPIE 5535, 137–142 (2004).

  20. 20

    Weitkamp, T. et al. Quantitative X-ray phase imaging with a grating interferometer. Opt. Express 13, 6296–6304 (2005).

  21. 21

    Born, M. & Wolf, E. Principles of Optics (Pergamon, Oxford, 1980).

  22. 22

    Henke, B. L., Gullikson, E. M. & Davis, J. C. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92. At. Data Nucl. Data Tables 54, 181–342 (1993).

  23. 23

    Pagot, E. et al. Quantitative comparison between two phase contrast techniques: diffraction enhanced imaging and phase propagation imaging. Phys. Med. Biol. 50, 709–724 (2005).

  24. 24

    Keith, D. W., Ekstrom, C. R., Turchette, Q. A. & Pritchard, D. E. An interferometer for atoms. Phys. Rev. Lett. 66, 2693–2696 (1991).

  25. 25

    David, C., Ziegler, E. & Nöhammer, B. Wet-etched diffractive lenses for hard X-rays. J. Synchrotron Radiat. 8, 1054–1055 (2001).

Download references


We gratefully acknowledge the assistance of C. Grünzweig in the measurements and P. R. Willmott for fruitful discussions.

Author information

Correspondence to Franz Pfeiffer.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Further reading